Jet engines for military and commercial applications demand improved efficiency, in terms of specific fuel consumption. The efficiency may be raised by increasing the exhaust gas temperature of the airflow entering the turbine stage of the engine. This increased temperature must be compensated for in terms of internal cooling of the nozzle and turbine blades of the turbine section. One method to cool the nozzles and turbine blades is to extract compressed air from the last compressor stage, prior to the combustion stage, cool this air, and re-inject it into the hollow cavities of the nozzles and turbine blades. The air may be cooled via an air-to-air heat exchanger that is located within the fan bypass annulus of the engine, in order to benefit from relatively colder temperature air flowing past the heat exchanger. Such a heat exchanger would typically have external fins, in order to increase the surface area of the exchanger, and to improve the external airflow mixing. In transferring heat to the fan bypass flow of the engine, the finned heat exchanger may typically include internal fluid passages for transporting the high pressure air extracted from a final compressor stage.